Elliptic curve isogeny class with Cremona label 714f (LMFDB label 714.e)

• Label: 714f
• Number of curves: $4$
• Conductor: $714$
• CM: no
• Rank: $1$

Elliptic curves in class 714f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
714.e4	714f1	\([1, 1, 1, 1, 101]\)	\(103823/4386816\)	\(-4386816\)	\([4]\)	\(192\)	\(-0.046597\)	\(\Gamma_0(N)\)-optimal
714.e3	714f2	\([1, 1, 1, -319, 2021]\)	\(3590714269297/73410624\)	\(73410624\)	\([2, 2]\)	\(384\)	\(0.29998\)
714.e2	714f3	\([1, 1, 1, -679, -3883]\)	\(34623662831857/14438442312\)	\(14438442312\)	\([2]\)	\(768\)	\(0.64655\)
714.e1	714f4	\([1, 1, 1, -5079, 137205]\)	\(14489843500598257/6246072\)	\(6246072\)	\([2]\)	\(768\)	\(0.64655\)

Rank

The elliptic curves in class 714f have rank \(1\).

Complex multiplication

The elliptic curves in class 714f do not have complex multiplication.

Modular form 714.2.a.f

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.